Decay of solutions in nonhomogeneous thermoelastic diffusion bars

Abstract

We consider a nonhomogeneous thermoelastic diffusion system in one space dimension where the coefficients are space-dependent. For Dirichlet, Neumann- and Robin-type boundary conditions the existence and uniqueness of solutions is proved by means of a strongly continuous semigroup of bounded operators associated to the system. Then, the exponential and polynomial decay of the solutions is discussed. We conclude by showing the impossibility of localization in time of the solutions.

Keywords:

• thermoelastic diffusion
• nonhomogeneous
• well-posedness
• exponential stability
• polynomial stability
• impossibility of localization in time.

AMS Subject Classifications:

• Primary 35B35
• Secondary 35B40

Acknowledgments

The authors would like to thank the Editor-in-chief and the anonymous referees for their useful and helpful comments and suggestions.